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Simplifying -2j2 + 7j = -1 Reorder the terms: 7j + -2j2 = -1 Solving 7j + -2j2 = -1 Solving for variable 'j'. Reorder the terms: 1 + 7j + -2j2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 7j + -2j2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -3.5j + j2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.5j + 0.5 + j2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.5j + j2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.5j + j2 = 0 + 0.5 -3.5j + j2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.5j + j2 = 0.5 The j term is -3.5j. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5j + 3.0625 + j2 = 0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5j + j2 = 0.5 + 3.0625 Combine like terms: 0.5 + 3.0625 = 3.5625 3.0625 + -3.5j + j2 = 3.5625 Factor a perfect square on the left side: (j + -1.75)(j + -1.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (j + -1.75) equal to 1.887458609 and -1.887458609.Subproblem 1
j + -1.75 = 1.887458609 Simplifying j + -1.75 = 1.887458609 Reorder the terms: -1.75 + j = 1.887458609 Solving -1.75 + j = 1.887458609 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + j = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + j = 1.887458609 + 1.75 j = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 j = 3.637458609 Simplifying j = 3.637458609Subproblem 2
j + -1.75 = -1.887458609 Simplifying j + -1.75 = -1.887458609 Reorder the terms: -1.75 + j = -1.887458609 Solving -1.75 + j = -1.887458609 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + j = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + j = -1.887458609 + 1.75 j = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 j = -0.137458609 Simplifying j = -0.137458609Solution
The solution to the problem is based on the solutions from the subproblems. j = {3.637458609, -0.137458609}
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